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17. Generalized D-Forms Have No Spurious Creases

Author

Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, Demaine, Erik D., Price, Gregory N., Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, Demaine, Erik D., and Price, Gregory N.

Abstract

A convex surface that is flat everywhere but on finitely many smooth curves (or seams) and points is a seam form. We show that the only creases through the flat components of a seam form are either between vertices or tangent to the seams. As corollaries we resolve open problems about certain special seam forms: the flat components of a D-form have no creases at all, and the flat component of a pita-form has at most one crease, between the seam’s endpoints., National Science Foundation (U.S.) (CAREER award CCF-0347776), United States. Dept. of Energy (grant DE-FG02-04ER25647), United States. Air Force Office of Scientific Research (grant FA9550-07-1-0538), National Science Foundation (U.S.) (Graduate Research Fellowship)

Published
2011

18. Generalized D-Forms Have No Spurious Creases

Author

Gregory N. Price, Erik D. Demaine, Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science, Demaine, Erik D., and Price, Gregory N.

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, Surface (mathematics), ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Geometry, 02 engineering and technology, Computer Science::Computational Geometry, 01 natural sciences, GeneralLiterature_MISCELLANEOUS, Theoretical Computer Science, Combinatorics, 0202 electrical engineering, electronic engineering, information engineering, Discrete Mathematics and Combinatorics, 0101 mathematics, Spurious relationship, Mathematics, ComputingMethodologies_COMPUTERGRAPHICS, Component (thermodynamics), 010102 general mathematics, Regular polygon, ComputingMilieux_PERSONALCOMPUTING, Tangent, 020207 software engineering, Smooth curves, Computational Theory and Mathematics, Computer Science - Computational Geometry, Geometry and Topology
Abstract

A convex surface that is flat everywhere but on finitely many smooth curves (or seams) and points is a seam form. We show that the only creases through the flat components of a seam form are either between vertices or tangent to the seams. As corollaries we resolve open problems about certain special seam forms: the flat components of a D-form have no creases at all, and the flat component of a pita-form has at most one crease, between the seam’s endpoints., National Science Foundation (U.S.) (CAREER award CCF-0347776), United States. Dept. of Energy (grant DE-FG02-04ER25647), United States. Air Force Office of Scientific Research (grant FA9550-07-1-0538), National Science Foundation (U.S.) (Graduate Research Fellowship)

Published
2009

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